Question

please don't answer unless you can do all parts, circle answer and show work please part

1)

A 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 3 ft/s, how fast will the foot be moving away from the wall when the top is 9 feet above the ground? The foot will be moving at ft/s. 2.87 (I got this but its wrong)

part 2)

Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 6 mi2/hrmi2/hr. How rapidly is radius of the spill increasing when the area is 10 mi2mi2? The radius is increasing at 9.38 (This is my answer I got and its incorrect) mi/hr.

part 3)

At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 18 knots and ship B is sailing north at 15 knots. How fast (in knots) is the distance between the ships changing at 6 PM? The distance is changing at 12.17 (Again my answer but its incorrect) knots. (Note: 1 knot is a speed of 1 nautical mile per hour.)

part 4)

A spherical balloon is inflated so that its volume is increasing at the rate of 3.8 ft3/minft3/min. How rapidly is the diameter of the balloon increasing when the diameter is 1.8 feet? The diameter is increasing at 1.8 (My answer but its incorrect) ft/min.

part 5)

A street light is at the top of a 18 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 6 ft/sec along a straight path. How fast is the tip of her shadow moving along the ground when she is 40 ft from the base of the pole?

ft/sec

How fast is the length of her shadow increasing?

ft/sec

part 6)

Suppose that for a company manufacturing calculators, the cost, and revenue equations are given by

C=70000+40x,R=400−x^2/30

where the production output in one week is x calculators. If the production rate is increasing at a rate of 500 calculators per week when the production output is 6000 calculators, find each of the following:

Rate of change in cost =

Rate of change in revenue =

Rate of change in profit =

Answer 1